Abstract
We consider five different types of systems of generalized vector variational inequalities and derive relationships among them. We introduce the concept of pseudomonotonicity for a family of multivalued maps and prove the existence of weak solutions of these problems under these pseudomonotonicity assumptions in the setting of Hausdorff topological vector spaces as well as real Banach spaces. We also establish the existence of a strong solution of our problems under lower semicontinuity for a family of multivalued maps involved in the formulation of the problems. By using a nonlinear scalar function, we introduce gap functions for our problems by which we can solve systems of generalized vector variational inequalities using optimization techniques.
| Original language | English |
|---|---|
| Pages (from-to) | 515-531 |
| Number of pages | 17 |
| Journal | Journal of Optimization Theory and Applications |
| Volume | 134 |
| Issue number | 3 |
| DOIs | |
| State | Published - Sep 2007 |
Bibliographical note
Funding Information:The first two authors were supported by SABIC and Fast Track Research Grants SAB-2006-05. They are grateful to the Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia for providing excellent research facilities.
Keywords
- Existence results for a solution
- Gap functions
- Lower semicontinuity
- Pseudomonotonicity
- Systems of generalized implicit vector variational inequalities
- Upper hemicontinuity
- ℋ-Hemicontinuity
ASJC Scopus subject areas
- Management Science and Operations Research
- Control and Optimization
- Applied Mathematics